In the related art, NOx-occlusion-reduction-type catalyst has been known, as catalyst for reducing and purifying NOx in exhaust to be emitted from an internal combustion engine. When the exhaust is in a lean atmosphere, the NOx-occlusion-reduction-type catalyst occludes NOx contained in the exhaust, and when the exhaust is in a rich atmosphere, the NOx-occlusion-reduction-type catalyst detoxifies and releases the occluded NOx with hydrocarbon contained in the exhaust by reduction and purification. For this reason when a NOx occlusion amount of the catalyst reaches a predetermined amount, it is necessary to periodically perform NOx purge of enriching the exhaust by exhaust pipe injection or post injection so as to recover a NOx occlusion capacity (for example, refer to PTLs 1 and 2).